A) \[9{{x}^{2}}-8{{y}^{2}}+18x-9=0\]
B) \[9{{x}^{2}}-8{{y}^{2}}-18x+9=0\]
C) \[9{{x}^{2}}-8{{y}^{2}}-18x-9=0\]
D) \[9{{x}^{2}}-8{{y}^{2}}+18x+9=0\]
Correct Answer: B
Solution :
Let (h, k)be point whose chord of contact w.r.t. hyperbola x2 - y2 = 9 is x = 9. We know Aat chord of contact of (h, k) w.r.t. hyperbola x2 - y2 = 9 is \[T=0\]\[\Rightarrow \]\[x(h)-y(k)-9=0\] But this is the same as equation of the line x = 9. \[\therefore \]\[h=1,k=0\] Again, equation of pair of tangents is \[{{T}^{2}}=S{{S}_{1}}\] \[\Rightarrow \]\[{{(x-9)}^{2}}=({{x}^{2}}-{{y}^{2}}-9)({{1}^{2}}-{{0}^{2}}-9)\] \[\Rightarrow \]\[{{x}^{2}}18x+81=({{x}^{2}}-{{y}^{2}}-9)(-8)\] \[\Rightarrow \]\[{{x}^{2}}-18x+81=-8{{x}^{2}}+8{{y}^{2}}+72\] \[\Rightarrow \]\[9{{x}^{2}}-8{{y}^{2}}-18x+9=0\]
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